 |
 |
|
|
| HAL: hal-00673832, version 1 |
| Detailed view |  Export this paper |
 |
|
|
| On the asymptotic behavior of the Nadaraya-Watson estimator associated with the recursive SIR method |
|
|
| Bernard Bercu 1, 2Thi Mong Ngoc Nguyen 1, 3 |
|
|
| (2012) |
|
|
|
| We investigate the asymptotic behavior of the Nadaraya-Watson estimator for the estimation of the regression function in a semiparametric regression model. On the one hand, we make use of the recursive version of the sliced inverse regression method for the estimation of the unknown parameter of the model. On the other hand, we implement a recursive Nadaraya-Watson procedure for the estimation of the regression function which takes into account the previous estimation of the parameter of the semiparametric regression model. We establish the almost sure convergence as well as the asymptotic normality for our Nadaraya-Watson estimator. We also illustrate our semiparametric estimation procedure on simulated data. |
|
|
|
|
|
|
|
|
|
|
|
| 1: | Institut de Mathématiques de Bordeaux (IMB) |
|
|
|
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
|
|
| 2: | ALEA (INRIA Bordeaux - Sud-Ouest) |
|
|
|
INRIA – Université de Bordeaux – CNRS : UMR5251 |
|
|
| 3: | CQFD (INRIA Bordeaux - Sud-Ouest) |
|
|
|
INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR5251 |
|
|
|
|
|
|
|
|
|
| Subject | : | Mathematics/Probability Mathematics/Statistics Statistics/Statistics Theory |
|
|
| Semi-parametric regression – recursive estimation – Nadaraya-Watson estimator – Sliced inversion regression |
|
|
|
| Attached file list to this document: | |||||
|
|||||
|
|
|
| hal-00673832, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00673832 | |
| oai:hal.archives-ouvertes.fr:hal-00673832 | |
| From: Bernard Bercu | |
| Submitted on: Friday, 24 February 2012 13:37:34 | |
| Updated on: Saturday, 25 February 2012 10:52:41 | |
